An Optimal Inequality for Warped Product Pointwise Semi-Slant Submanifolds in Complex Space Forms
In this paper, we utilize advanced optimization techniques on Riemannian submanifolds to establish two distinct inequalities concerning the generalized normalized <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi...
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2025-03-01
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| description | In this paper, we utilize advanced optimization techniques on Riemannian submanifolds to establish two distinct inequalities concerning the generalized normalized <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>δ</mi></semantics></math></inline-formula>-Casorati curvatures of warped product pointwise semi-slant (WPPSS) submanifolds within complex space forms. We further identify the precise conditions under which these inequalities attain equality, providing valuable insights into their geometric and structural significance. Additionally, we also present results involving harmonic and Hessian functions, revealing a broader connection between curvature properties and analytic functions. |
| format | Article |
| id | doaj-art-618662ee674948469d5ab79fdcfe0184 |
| institution | DOAJ |
| issn | 2075-1680 |
| language | English |
| publishDate | 2025-03-01 |
| publisher | MDPI AG |
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| series | Axioms |
| spelling | doaj-art-618662ee674948469d5ab79fdcfe01842025-08-20T02:42:45ZengMDPI AGAxioms2075-16802025-03-0114321310.3390/axioms14030213An Optimal Inequality for Warped Product Pointwise Semi-Slant Submanifolds in Complex Space FormsMd Aquib0Department of Mathematics and Statistics, College of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), P.O. Box 65892, Riyadh 11566, Saudi ArabiaIn this paper, we utilize advanced optimization techniques on Riemannian submanifolds to establish two distinct inequalities concerning the generalized normalized <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>δ</mi></semantics></math></inline-formula>-Casorati curvatures of warped product pointwise semi-slant (WPPSS) submanifolds within complex space forms. We further identify the precise conditions under which these inequalities attain equality, providing valuable insights into their geometric and structural significance. Additionally, we also present results involving harmonic and Hessian functions, revealing a broader connection between curvature properties and analytic functions.https://www.mdpi.com/2075-1680/14/3/213Casorati curvaturesemi-slant submanifoldwarped product submanifoldcomplex space formharmonic functionHessian function |
| spellingShingle | Md Aquib An Optimal Inequality for Warped Product Pointwise Semi-Slant Submanifolds in Complex Space Forms Axioms Casorati curvature semi-slant submanifold warped product submanifold complex space form harmonic function Hessian function |
| title | An Optimal Inequality for Warped Product Pointwise Semi-Slant Submanifolds in Complex Space Forms |
| title_full | An Optimal Inequality for Warped Product Pointwise Semi-Slant Submanifolds in Complex Space Forms |
| title_fullStr | An Optimal Inequality for Warped Product Pointwise Semi-Slant Submanifolds in Complex Space Forms |
| title_full_unstemmed | An Optimal Inequality for Warped Product Pointwise Semi-Slant Submanifolds in Complex Space Forms |
| title_short | An Optimal Inequality for Warped Product Pointwise Semi-Slant Submanifolds in Complex Space Forms |
| title_sort | optimal inequality for warped product pointwise semi slant submanifolds in complex space forms |
| topic | Casorati curvature semi-slant submanifold warped product submanifold complex space form harmonic function Hessian function |
| url | https://www.mdpi.com/2075-1680/14/3/213 |
| work_keys_str_mv | AT mdaquib anoptimalinequalityforwarpedproductpointwisesemislantsubmanifoldsincomplexspaceforms AT mdaquib optimalinequalityforwarpedproductpointwisesemislantsubmanifoldsincomplexspaceforms |